The Theory of Automatic Regulators. 
283 
rise above the normal, according to the load, keeping it constant, say, at 
the feeding points. 
In order to avoid sparking at the relay contacts, condensers are joined 
across them. In addition the contacts should be carefully cleaned every 
morning if good working is to be expected. 
Theory ojp the Tireill REauLATOR, — Fig. 7 shows the simplified 
connections of this regulator. 
Let X = 0 he the position of core and of lever Aj, for which the spring 
fi has the tension 0. The pull of the spring is a function of the elongation, 
or of X, {. e. = x, where is some constant. 
For a definite position of the magnetic pull is proportional to the 
square of the flux density, and thus to the square of the voltage, or Fo^K^V^ 
where Kg is another constant. For different values of the voltage the core 
will therefore take up different positions, and hence to each value of the 
voltage corresponds a definite x. Thus to V^, V^, correspond 
Xq, x^, X2 Xn respectively. It is also possible, although not essential, to 
make = O, which means that the magnetic pull is independent of x when 
the voltage is constant. 
Assume now that the lever h^ is kept in a jmrticular position, and that 
h^ is moved clockwise until contacts K^K^ close, at which instant the dis- 
placement of core is x^. For any other position the contacts are open and 
the resistance r^ is inserted, giving the voltage Ygo ^it the exciter terminals 
(see fig. 8), the lowest possible. For this voltage the lever h^ must rotate 
clockwise, as F^ overcomes F._>, and hence r^ is short-circuited. Let at this 
instant t = 0. The pressure now rises along the exponential curve, the 
curve depending upon the value of a., tending towards a final value y„. At 
time ti the pressure is reached, and as the displacement is a^^, which corre- 
sponds to Vj, the lever is in equilibrium. But the exciting current, and 
hence the exciter pressure, rise still further, so that from now onwards the 
magnetic pull will predominate, contacts K^K^ are separated and r^ is re- 
inserted. The exciter current and voltage drop again. 
The separation occurs at time t^, for which the pressure has the 
value Yj^ -I- S. 8 must have some definite value, as masses have to be 
accelerated. At time t.^, is again reached (see fig. 8), but the pressure 
is on the downward grade and tends to reach Ygo which corresponds to 
the insertion of r^. But below V;^ the spring exerts itself ; however, a 
little time will elapse before the contacts K^K.) are closed again, which 
occurs at time t^. The pressure has the value — 8. The play 
then commences afresh, showing that the lever h^^ vibrates all the time 
while the exciting current and exciter pressure pulsate round some mean 
value Yj. The mean forces acting on the lever are in equilibrium, and no 
pressure is exerted on lever /t^ except a small contact pressure. From the 
